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Function Inverse - Function of Function Inverse to X

Level 1

This topic explores the mathematical concept of function compositions and inversions. Specifically, it focuses on finding the result of compositions where functions are applied to their own inverses, across multiple levels of complexity. The questions generally ask for the outcome when an inverse function evaluates its paired function (e.g., m(n(x)), y(n(x)), m(c(x)), and others). The possible answers are given in various mathematical expressions, such as x, x², 1/x, etc., and students must select the correct one based on the given functions and their compositions.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Function Inverse - Function of Function Inverse to X Worksheet

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Function Inverse - Function of Function Inverse to X
1
What is the result of b(d(x))?
A LaTex expression showing \text{given: }\\b(x) = d to the power of -1 (x)\\\\\text{what is }b(d(x))
a A LaTex expression showing 1 over x
b A LaTex expression showing 1
c A LaTex expression showing x to the power of -1
d A LaTex expression showing x to the power of 2
e A LaTex expression showing x
2
What is the result of b(y(x))?
A LaTex expression showing \text{given: }\\b(x) = y to the power of -1 (x)\\\\\text{what is }b(y(x))
a A LaTex expression showing 1
b A LaTex expression showing x
c A LaTex expression showing 1 over x
d A LaTex expression showing x to the power of 2
e A LaTex expression showing x to the power of -1
3
What is the result of p(r(x))?
A LaTex expression showing \text{given: }\\p(x) = r to the power of -1 (x)\\\\\text{what is }r(p(x))
a A LaTex expression showing 1 over x
b A LaTex expression showing x to the power of 2
c A LaTex expression showing x
d A LaTex expression showing 1
e A LaTex expression showing x to the power of -1
4
What is the result of d(r(x))?
A LaTex expression showing \text{given: }\\d(x) = r to the power of -1 (x)\\\\\text{what is }r(d(x))
a A LaTex expression showing x to the power of -1
b A LaTex expression showing x to the power of 2
c A LaTex expression showing x
d A LaTex expression showing 1
e A LaTex expression showing 1 over x
5
What is the result of b(r(x))?
A LaTex expression showing \text{given: }\\b(x) = r to the power of -1 (x)\\\\\text{what is }b(r(x))
a A LaTex expression showing x
b A LaTex expression showing 1 over x
c A LaTex expression showing 1
d A LaTex expression showing x to the power of -1
e A LaTex expression showing x to the power of 2
6
What is the result of z(d(x))?
A LaTex expression showing \text{given: }\\z(x) = d to the power of -1 (x)\\\\\text{what is }z(d(x))
a A LaTex expression showing 1
b A LaTex expression showing x
c A LaTex expression showing 1 over x
d A LaTex expression showing x to the power of -1
e A LaTex expression showing x to the power of 2
7
What is the result of y(d(x))?
A LaTex expression showing \text{given: }\\y(x) = d to the power of -1 (x)\\\\\text{what is }y(d(x))
a A LaTex expression showing x to the power of 2
b A LaTex expression showing x
c A LaTex expression showing x to the power of -1
d A LaTex expression showing 1
e A LaTex expression showing 1 over x
8
What is the result of d(p(x))?
A LaTex expression showing \text{given: }\\d(x) = p to the power of -1 (x)\\\\\text{what is }d(p(x))
a A LaTex expression showing x to the power of 2
b A LaTex expression showing x to the power of -1
c A LaTex expression showing 1
d A LaTex expression showing 1 over x
e A LaTex expression showing x