Question

If $f(x)=3x+5$ and $g(x)=x^2-1,$ then (fog) $(x^2-1)$ is equal to

• A. $3x^4-3x+5$
• B. $3x^4-6x^2+5$
• C. $6x^4+3x^2+5$
• D. $6x^4-6^x+5$
• E. $3x^2+6^x+4$

Answer 1

Answer: (B)

$\because f(x)=3x+5$
and $g(x)=x^2-1$
$\therefore$ fog $\left(x^2-1\right)=f\left[g\left(x^2-1\right)\right]$
$=f\left[{\left(x^2-1\right)}^2-1\right]$
$=f\left[x^4-2x^2+1-1\right]=f\left[x^4-2x^2\right]$
$=3\left(x^4-2x^2\right)+5$
$=3x^4-6x^2+5$