Answer: 341
=====================================================
Step-by-step explanation:
When two letters are placed together without any space between them, this implies multiplication.
gf = g times f
So we'll be multiplying the functions g and f.
There are two ways to approach this problem.
----------------------------------------------
Method 1
First we need to find f(4) and g(4)
f(x) = 2x+3
f(4) = 2*4+3
f(4) = 8+3
f(4) = 11
g(x) = 2x^2-1
g(4) = 2(4)^2-1
g(4) = 2(16)-1
g(4) = 32-1
g(4) = 31
Now we multiply the results
gf(4) = g(4)*f(4)
gf(4) = 11*31
gf(4) = 341
----------------------------------------------
Method 2
We'll multiply g(x) with f(x) like so
gf(x) = g(x)*f(x)
gf(x) = (2x^2-1)*(2x+3)
gf(x) = 2x^2*(2x+3) - 1(2x+3) .... distribute
gf(x) = 4x^3+6x^2-2x-3 .... distribute again
Now plug in x = 4
gf(x) = 4x^3+6x^2-2x-3
gf(4) = 4(4)^3+6(4)^2-2(4)-3
gf(4) = 4(64)+6(16)-2(4)-3
gf(4) = 256+96-8-3
gf(4) = 341
We get the same result. Method 1 may be the better method, but it will depend on your preference.