Assume f(x) =-2x + 8 and g(x) = 3x. What is the value of (g o f)(3)?

Answer 1

The notation (g 0 f) (3) means that you will first evaluate f(3) , and if that result is in the domain of g, you will evaluate g ( f(3))

In this case: f(3) = -2x3 + 8 = -6 + 8 = 2

and g (f(3)) = g(2) = 3x2 = 6

Answer 2

g_ºf means g(f(x))

When you are asked to find g(1) it means plug "1" into the function rule so 3(1) = 3

When you are asked to find g(a) it means plug "a" into the function rule so 3(a) = 3a

If you want to find g(f(x)) then you plug the function f(x), which is "-2x + 8" into the function rule so:

3(-2x + 8) = -6x + 24

So g(f(x)) = -6x + 24

and g(f(3)) = -6(3) + 24 = -18 + 24 = 6

There is a "short cut". You can first figure out what f(3) is and then plug the result into g(x)

f(3) = -2(3) + 8 = 2

then g(2) = 3(2) = 6

Answer 3

Hi Kafayat,

In order to find g(f(3)), we first must substitute the f(x) into the g(x) expression, as follows;

g(f(x)) = 3(-2x + 8)

Then we can plug in 3 for x:

g(f(3)) = 3(-2(3) + 8) = 3(-6 + 8) = -18 + 24 = 6