If $f(x)=5-3x$ and $g(x)=x^2-1$ , what is $f(g(x))$ and $g(f(x))$ ?

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Answer 1 · 2016-09-07T16:38:39

$f(g(x))=8-3x^2$ and

$g(f(x))=9x^2-30x+24$

As $f(x)=5-3x$ and $g(x)=x^2-1$

$f(g(x))=5-3×(x^2-1)$

= $5-3x^2+3$

= $8-3x^2$ and

$g(f(x))=(5-3x)^2-1$

= $25-30x+9x^2-1$

= $9x^2-30x+24$

If f(x)=5-3xf(x)=5-3x and g(x)=x^2-1g(x)=x^2-1, what is f(g(x))f(g(x)) and g(f(x))g(f(x))?