Question

If f (x) = 5 x minus 25 and g (x) = one-fifth x + 5, which expression could be used to verify g(x) is the inverse of f(x)?

Answer 1

Answer:

$f(g(x))=x$

Step-by-step explanation:

Given a certain function $f(x)$, and then its inverse function $f^{-1}(x)$, the following expression is valid:

$(f\cdot f^{-1})(x)=x$

where the expression

$(f\cdot f^{-1})(x)=f(f^{-1}(x))$

indicates the composite function.

In this problem, we have:

$f(x)=5x-25$

And then, its inverse function is

$g(x)=\frac{1}{5}x+5$

To verify that g(x) is the inverse of f(x), the following expression must be true:

$f(g(x))=x$

Substituting the expression of g(x) into f(x), we find that:

$f(g(x))=5g(x)-25=5(\frac{1}{5}x+5)-25=x+25-25=x$

So, g(x) is the inverse of f(x).

Answer 2

Answer:

F(g(x))=x

Step-by-step explanation: