Let g(x) = cos(x/2) - 3x. Let f(x) = 2x + 5. What is g(f(x))?

f = 2

Explanation:

g(x) = cos(x/2) - 3x=w where w=-3.5 or -1 or -38.5

13– (13/2)-3*13=-3.5 (1st d value of g(x))

-1-(-1/2)-3*(-1)=-1 (the 2nd possible value)

g(x) = cos(x/2) - 3x=-1 where the first x=13 and the 2nd one=-1

where the first x=-1 and the 2nd one=-38.5 (the 3rd value)

g(x) = cos(x/2) - 3x)=0 where cos(x/2=-3.5

g(f(x)) = cos(f(x)/2) - 3 aka 0.5 f(x) = cos(2x+5 aka 7x) (x/2 - 3 =aka -1 );

(2x+5) = 7x by definition but the equation has to be set to 7 to find x)

(7x/2 -6x=0) -7 on both sides

x/2–6x=-7

x/2= 13

26/2=x

x=13 (these values are set up for 2x+5=7.

13-(-7)=-7

13-6+-1=-7

the 2nd x=-1

gfx=cos*2*x i.e cos*2*13 or cos*2*-1

cos*2*13=26

cos*2*(-1)=-1

cos=1

(cos*2*13)=the 1st gfx value=26 basically.

( cos*2*(-13)=-26 (the 2nd gfx value)

cos*2*(-1)=-`1 (the 3rd gfx value)

f=2

hope this helped!