Two functions f and g are defined by
f:x = x^2 + 3
g:x = 2x+1
Find the function fg
Please help and show all working out,i got the answer for it but i really don't understand it!!!
Thank You
To find the function fg, we need to find the composition of the functions f and g, which means substituting the expression of g into the variable x in function f.
Given:
f(x) = x^2 + 3
g(x) = 2x + 1
To find fg, substitute g(x) into f(x):
fg(x) = f(g(x))
Step 1: Replace x in f(x) with g(x):
fg(x) = (g(x))^2 + 3
Step 2: Substitute g(x) into the equation:
fg(x) = (2x + 1)^2 + 3
Step 3: Simplify the equation:
fg(x) = (2x + 1)(2x + 1) + 3
= 4x^2 + 2x + 2x + 1 + 3
= 4x^2 + 4x + 4
Therefore, the function fg is given by:
fg(x) = 4x^2 + 4x + 4