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## High school math (India)

### Course: High school math (India)>Unit 7

Lesson 1: Relations and functions

# Intro to composing functions

This video is about composing functions, which is the process of building up a function by composing it from other functions. It explains how to evaluate the composition of functions step by step, using examples with three different function definitions: f (x), g(t), and h(x). Created by Sal Khan.

## Want to join the conversation?

• could you still answer f(g(x)) without knowing what "x" is? •   Yes. You can literally plug in the whole equation for g(x) in for f(x). For example:

f(x) = 2x + 1 and g(x) = 4/x

Then to solve for f(g(x)), you would plug in g(x) (the whole formula), in to f(x) for x. So...

f(g(x)) = 2(4/x) + 1 = 8/x + 1

This is just a simple example but you can do it with many more complicated formulas as well.
For example:
(given f(x) = 2x+3 and g(x) = -x^2 + 5
( f o g)(x) = f (g(x))
= f (–x^2 + 5)
= 2(g(x)) + 3
= 2(–x^2 + 5) + 3
= –2x^2 + 10 + 3
= –2x^2 + 13

Yes I know that these formulas are not as complicated as many people doing Algebra 2 could do, but I was just giving another example...

Hope this helps... :)
• can a function have more than one variable? like: f(a,b) or something •  Absolutely! A function with more than one variable would be called a multivariable function. and that is actually the correct way of notating it! A function with 2 variables would make a 3D object, 3 would make a 4D object, etc. Great question!
• will i need this for real life. plzzz help i need to kno •   Yes; say that I sell cars. In the function f(x) = y, the input (or x) is the number of cars being made in the year and the output (or y) is the price one needs to sell a car for. And then I will need to calculate the least amount of cars I would have to sell in order to earn enough money to pay my employees. The price of the car in that year will be P and the number of cars I will need to sell will be S, so I will now have a new function called g(P) = S.
However, it's too much unnecessary work for me to have those two separated because P, the price one needs to sell a car for, equals my definition of y, which equals f(x). So instead of going through two functions, I can now use g(f(x)) to find out how many cars I need to sell in the least in each year.
• Hey guys
Is it necessary to complete Algebra 2 before staring Precalculus ? • At where did you get (-3)^2-1 from? • WHAT IS THIS, I'm totally CONFUSED- • I have a question that is more general. I'm taking Precalculus next year, and was planning on studying in advance through Khan Academy. Has anyone taken Precalculus before? If so, does the curriculum in Khan Academy align with what is being taught at school? • Precalc Honors for me included topics such as:
Graphing linear, exponential, quadratics, cubics, quartics, stuff with higher degrees, logs, natural logs, powers of e.
Solving inequalities, factoring, difference of squares, difference quotient, stretch/shrink of graphs, vertical/horizontal shifts of graphs, reflections of graphs, horizontal/vertical asymptotes, properties of logs, solving logs, unit circle, radians, degrees, linear velocity, angular velocity, graphing trig functions, angle of depression/elevation, domain/range of trig functions, solving triangles, rule of sines, rule of cosines, equations/graphing/rules of: roses, limacons, cardioids, parabolas, ellipses, hyperbolas, and parametrics. Limits, sigma notation, geometric and arithmetic, half life, apert formula, a=pe(1+r/n)^nt thing, explicit/recursive.
This isn't a comprehensive list, since I don't recall everything, and also what I learn may not be what you learn, but this should give you a general idea.
• is the chart and graph the same for each example? • Does learning function only helps us in computer programming? • Absolutely not! Learning functions is essential to mathematics and thus the sciences and engineering disciplines. Creating functions can be useful for things as simple as grocery shopping, assigning probability to something, and so forth! To be able to turn the real world phenomena into a function is the height of mathematical power. 