Question

The function f and g are defined by :

f:x --> 3x+1
g:x --> 9-x

Determine the expression for the function gf(x) .

Answer 1

g(f(x)=9-(3x+3)=6-3x

Answer 2

how do u get the 3 ?

Answer 3

[AI-generated answer — Explain Bot]

To determine the expression for the function gf(x), we need to calculate the composition of the functions g and f.

The composition of two functions means evaluating one function and then using the output of that function as the input for the other function.

In this case, the function g(x) takes an input x and subtracts it from 9, while function f(x) takes an input x, multiplies it by 3, and then adds 1.

So to find the expression for gf(x), we first evaluate f(x), and then use the output as the input for g(x).

Let's substitute the expression for f(x) into g(x):

g(f(x)) = g(3x + 1)

Now, substitute x into the expression for g(x):

g(f(x)) = 9 - (3x + 1)

Simplify the expression by distributing the negative sign:

g(f(x)) = 9 - 3x - 1

Combine like terms:

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

Therefore, the expression for the function gf(x) is -3x + 8.