Question

Maggie claims that the function g(x) = - 4 is the inverse of the function of f(0) = 3a + 4.
Which statement provides a correct analysis of Maggie's claim?
Maggie's claim is correct because if you add 4 to g(x) and then multiply it by 3 you get
f(x)
Maggie's claim is correct because when g(x) is substituted into every occurrence of x
O in f(x), f(g(x)) = x, and when f(x) is substituted into every occurrence of x in g(x),
g(f(x)) = x
Maggie's claim is incorrect because when g(x) is substituted into every occurrence of
O x in f(x). ; therefore, g(x) is not the inverse of f(x), f(g(x))=x-8; therefore, g(x) is not the
inverse of f(x)
Maggie's claim is incorrect because when g(x) is substituted into every occurrence of
x in f(x), f(g(x)) = x; therefore, g(x) is not the inverse of f(x).

Answer 1

The inverse of a function reverses the operation of a function

The statement that provides the correct analysis of Maggie's claim is the following option;

Maggie's claim is incorrect because when g(x) is substituted into every occurrence of x in f(x), f(g(x)) = x - 8; therefore, g(x) is not the inverse of f(x)

Question: The functions in the question are presented as follows;

$g(x) = \dfrac{x}{3} - 4$

f(x) = 3·x + 4

Required:

The statement that provides a correct analysis of Maggie's claim

Solution:

The inverse of f(x) is found as follows;

y = 3·x + 4

$x = \dfrac{y - 4}{3}$

Therefore;

$f^{-1}(x) = \dfrac{x - 4}{3}$

The inverse of a function above was found by making x the subject of the

function f(x), therefore, when the inverse f⁻¹(x) is substituted into all

occurrence of x in f(x), we get x

However, when g(x) is substituted into every occurrence of x in g(x), we get;

$f \left (g(x) \right) = 3 \times \left (\dfrac{x}{3} - 4 \right)+ 4 = x - 8 \neq x$

Therefore, the given function g(x) is not the inverse of the function f(x) and the correct option is as follows;

Maggie's claim is incorrect because when g(x) is substituted into every occurrence of x in f(x), f(g(x)) = x - 8; therefore, g(x) is not the inverse of f(x)

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