Question

F(x)=2x and g(x)=x2+4; find i) gof ii) fog iii) f(g(2))

Answer 1

To find gof, plug g(x) into f(x) and simplify. To find fog, plug f(x) into g(x) and simplify. To evaluate f(g(2)), first evaluate g(2), then plug this result into f(x).

Step-by-step explanation:

i) To find gof, we substitute the function g(x) into f(x). So gof(x) is equal to f(g(x)). Plugging in g(x) = x^2 + 4, we get:

gof(x) = f(g(x)) = f(x^2 + 4) = 2(x^2 + 4) = 2x^2 + 8

ii) To find fog, we substitute the function f(x) into g(x). So fog(x) is equal to g(f(x)). Plugging in f(x) = 2x, we get:

fog(x) = g(f(x)) = g(2x) = (2x)^2 + 4 = 4x^2 + 4

iii) To find f(g(2)), we first evaluate g(2) by plugging in x = 2 into g(x):

g(2) = 2^2 + 4 = 4 + 4 = 8

Then, we plug this result into f(x):

f(g(2)) = f(8) = 2(8) = 16