Question

For ​f(x)=x+5 and ​g(x)=4x+5​, find (fog)(x), (gof)(x), (fog)(1), (gof)(1)

Answer 1

To find (fog)(x) and (gof)(x), substitute g(x) into f(x) and f(x) into g(x) respectively. (fog)(1) = 14 and (gof)(1) = 29.

Step-by-step explanation:

To find (fog)(x) and (gof)(x), we need to substitute g(x) into f(x) and f(x) into g(x) respectively. For (fog)(x), we substitute g(x) into f(x):

fog(x) = f(g(x)) = f(4x+5) = (4x+5) + 5 = 4x + 10.

For (gof)(x), we substitute f(x) into g(x):

gof(x) = g(f(x)) = g(x+5) = 4(x+5)+ 5 = 4x + 20 + 5 = 4x + 25.

To find (fog)(1), we substitute x = 1 into fog(x):

fog(1) = 4(1) + 10 = 14.

To find (gof)(1), we substitute x = 1 into gof(x):

gof(1) = 4(1) + 25 = 29.