Precalculus Examples

$(f g) (x) = f (x^{2} - 3)$

Step 1

Simplify.

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Step 1.1

Simplify both sides of the equation.

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Step 1.1.1

Multiply $f g$ by $x$ .

$f g (x) = f (x^{2} - 3)$

Step 1.1.2

Multiply $f g$ by $x$ .

$f g x = f (x^{2} - 3)$

Step 1.2

Reduce by cancelling the common factors.

$f g x = x^{2}$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(x)$ of the left side $(f g x)$ equals the exponent $(2)$ .

$\log_{x} (f g x) = 2$