Find f(g(x)) f(x)=2x^2-x g(x)=x^-2

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

Set up the composite result function.

$f (g (x))$

Evaluate $f (g (x))$ by substituting in the value of $g$ into $f$ .

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

Simplify each term.

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Multiply the exponents in ${(x^{- 2})}^{2}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $- 2$ by $2$ .

$f (x^{- 2}) = 2 x^{- 4} - (x^{- 2})$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$f (x^{- 2}) = 2 (\frac{1}{x^{4}}) - (x^{- 2})$

Combine $2$ and $\frac{1}{x^{4}}$ .

$f (x^{- 2}) = \frac{2}{x^{4}} - (x^{- 2})$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$f (x^{- 2}) = \frac{2}{x^{4}} - \frac{1}{x^{2}}$

Find f(g(x)) f(x)=2x^2-x g(x)=x^-2

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