Question

If f(x) = $x^n$ then the graph of g(x) =$x^{\frac{1}{n}}$ is the mirror image of f(x) about y = x.

• A. True
• B. False

Answer 1

The correct option is A

True

If the graph of f(x) is the mirror image of g(x) about y = x, it means f(x) is the inverse of g(x). So we just have to check if g(x) = $x^{\frac{1}{n}}$ is the inverse of f(x) = $x^n$.

To find the inverse of a function f(x), write

y = f(x) . . . . . . (1)

Express x in terms of y using (1).

Replace y with x in the same expression. In our case,

y = $x^n$

$\Rightarrow$ x = $y^{\frac{1}{n}}$

We will replace y with x to get g(x)

$\Rightarrow$ g(x) = $x^{\frac{1}{n}}$

We saw that $x^n$and $y^{\frac{1}{n}}$ are inverses of each other. So their graphs will be mirror image of each other about y = x.