if f(x) =x+3/7 and g(x) =4+5x find (gof) (x)
Replace the x is the f(x) by the values for g(x)
for the x is the f(x) you would write 4 + 5x + 3/7
I don't know if the problem is
(x+3) all divided by 7
or if it is x added to 3/7
(g◦f)(x) = g(f(x))
g(x) = 4+5x, so
g(f) = 4 + 5f
= 4+5(x+3/7)
and we are back to Dr. Jane's question
Yes it is (x+3) all divided by 7
To find (gof)(x), we need to compose the functions g and f.
In other words, we need to substitute the function g into the function f.
First, let's find the expression for g(f(x)):
g(f(x)) = g(x + 3/7)
Next, let's substitute the expression for g(x) into the above equation:
g(f(x)) = 4 + 5(x + 3/7)
Now, let's simplify the equation:
g(f(x)) = 4 + 5x + 15/7
To write the equation in a simplified form, we can combine the constant terms:
g(f(x)) = (4 + 15/7) + 5x
To further simplify the constant terms, we can convert 4 to 28/7:
g(f(x)) = (28/7 + 15/7) + 5x
Adding the numerators, we get:
g(f(x)) = 43/7 + 5x
Therefore, (gof)(x) = 43/7 + 5x.