If f(x) = x^2- 2, how do you find expressions for f(-x)?

2 Answers
Apr 9, 2018

$f \left(- x\right) = {x}^{2} - 2 = f \left(x\right)$

Explanation:

$f \left(- x\right) = {\left(- x\right)}^{2} - 2 = {x}^{2} - 2$

Apr 9, 2018

see solution process below;

Explanation:

I think you mean't, ${f}^{-} 1 \left(x\right)$ which is the inverse of $f \left(x\right)$

But if its, $f \left(- x\right)$ it should be $- \left({x}^{2} - 2\right)$

Hence;

$f \left(x\right) = {x}^{2} - 2$

$f \left(- x\right) = - \left({x}^{2} - 2\right)$

$f \left(- x\right) = - {x}^{2} + 2 \mathmr{and} 2 + {x}^{2}$

But if its $f {\left(x\right)}^{-} 1$

Let, $f \left(x\right) = y$

$y = {x}^{2} - 2$

Making $x$ the subject of formula;

${x}^{2} - 2 = y$

${x}^{2} = y + 2$

$x = \sqrt{y + 2}$

Therefore;

$f {\left(x\right)}^{-} 1 = \sqrt{x + 2}$