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

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Answer 1 · 2018-04-09T12:02:01

$f (- x) = x^{2} - 2 = f (x)$ $f(-x)=x^2-2=f(x)$

$f (- x) = {(- x)}^{2} - 2 = x^{2} - 2$ $f(-x)=(-x)^2-2=x^2-2$

Answer 2 · 2018-04-09T13:10:18

see solution process below;

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

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

Hence;

$f (x) = x^{2} - 2$ $f(x)=x^2- 2$

$f (- x) = - (x^{2} - 2)$ $f(-x)=-(x^2-2)$

$f (- x) = - x^{2} + 2 or 2 + x^{2}$ $f(-x) =-x^2+ 2 or 2 + x^2$

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

Let, $f (x) = y$ $f(x)= y$

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

Making $x$ $x$ the subject of formula;

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

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

$x = \sqrt{y + 2}$ $x = sqrt(y + 2)$

Therefore;

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

If f(x)=x2−2f(x) = x^2- 2, how do you find expressions for f(-x)?