Let $f(x) = 3x - 4$ and $g(x) = x^2 - 2$ , what is the value of $f(g(2))$ and $f(g(x))$ ?

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Answer 1 · 2016-03-04T22:46:19

$color(blue)(f(g(2))=2)$
$color(white)(.)$
$color(blue)(g(f(x))= -15x+14)$

Assuming you mean:
$f(x)=3x-4$
$g(x)=x^2-2$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("To determine "f(g(2)))$

$g(2)=2^2-2" " =" "4-2" "=" "2$

$f(g(2))=3(2)-4" " =" "6-4" "=" "2$

$color(blue)(f(g(2))=2)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("To determine "g(f(x)))$

Given that $f(x)=3x-4$ then

$g(f(x))= (3x-4)^2-2$

$g(f(x))= (9x-24x+16)-2$

$color(blue)(g(f(x))= -15x+14)$

Let f(x) = 3x - 4f(x) = 3x - 4 and g(x) = x^2 - 2g(x) = x^2 - 2, what is the value of f(g(2))f(g(2)) and f(g(x))f(g(x))?