Question

If f(x)=(x+3)³+4 let g(x)=f(x+1)-2 find when g(x)=12

Answer 1

Answer:

$x=\sqrt[3]{10}-2$

Step-by-step explanation:

The composite function (f(x+1)) is moved in the x-axis by -1, you know this by solving x+1=0.

The equivalent expresion for f(x+1) is

$f(x+1)= (x-1+3)^{3}+4$

$f(x+1)=(x+2)^{3}+ 4$

Eval the above expression in g(x)

$g(x)=(x+2)^{3}+4-2$

We must find x that gives g(x)=12

The equation is the following

$12=(x+2)^{3}+2$

Grouping terms>

$(x+2)^{3} =10$

To solve for x, must apply cubic root in both sides of equation:

$\sqrt[3]{(x+2)^{3} } =\sqrt[3]{10}$

it then turns in the following>

$x+2=\sqrt[3]{10}$

Giving the stated answer