If f(x)=x, g(x)=x^2 and h(x)=x^3, then find [(h ∘g) ∘f](x) (1) x (2) x^2 (3) x^3 (4) x^6

Name: Problem 55, Chapter 6: The IIT Foundation series of Mathematics Class
Uploaded: 2021-08-06T09:31:22-08:00
Duration: 1 min 16 s
Channel: Nidhi Singhi
Description: If f(x)=x, g(x)=x^2 and h(x)=x^3, then find [(h ∘g) ∘f](x) (1) x (2) x^2 (3) x^3 (4) x^6

step 1 Hello students. In this question, we are given F of X equals to X and G of X is given to be equa

If f(x)=x, g(x)=x^2 and h(x)=x^3, then find [(h ∘g) ∘f](x)...

If $\mathrm{f}(\mathrm{x})=\mathrm{x}, \mathrm{g}(\mathrm{x})=\mathrm{x}^{2}$ and $\mathrm{h}(\mathrm{x})=\mathrm{x}^{3}$, then find $[(\mathrm{h} \circ \mathrm{g}) \circ \mathrm{f}](\mathrm{x})$
(1) $\mathrm{x}$
(2) $x^{2}$
(3) $\mathrm{x}^{3}$
(4) $\mathrm{x}^{6}$

Key Concepts

Function Composition

Function composition is the process of applying one function to the result of another. It involves combining two or more functions such that the output of one function becomes the input for the next. Understanding function composition is crucial because it allows you to build complex operations by sequentially applying simpler ones. The notation (h ? g)(x) means that you first apply the function g to x and then apply the function h to the result of g(x).

Identity Function

An identity function is a type of function that returns its input without any modification. It is typically represented as f(x) = x. In the context of function composition, an identity function serves as a neutral element, meaning that composing any function with the identity function leaves the function unchanged. This concept simplifies the process of combining functions by not altering the input it receives.

Power Functions and Properties of Exponents

Power functions are functions where the input variable is raised to a constant exponent, such as x² or x³. The properties of exponents, like (x^a)^b = x^(a × b), are fundamental when composing power functions. When you compose functions that involve exponents, these properties help simplify the result by allowing you to combine the exponents multiplicatively, which is essential for correctly computing the overall function.

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