1. Part A.) For the f(x) = 5x + 8 and g(x) = x – 3. Calculate (f o g)(x)
Part B.) f(x) = 3x + 5 and g(x) = x². Calculate (f o g)(-3)
To calculate (f o g)(x), also known as the composition of two functions, you need to substitute the expression for g(x) into f(x).
Part A:
Given f(x) = 5x + 8 and g(x) = x - 3, we can find (f o g)(x) by substituting g(x) into f(x) and simplifying:
(f o g)(x) = f(g(x))
= f(x - 3)
= 5(x - 3) + 8
= 5x - 15 + 8
= 5x - 7
Therefore, (f o g)(x) = 5x - 7.
Part B:
Given f(x) = 3x + 5 and g(x) = x², we need to find (f o g)(-3) by substituting -3 for x in (f o g)(x):
(f o g)(-3) = f(g(-3))
= f((-3)²)
= f(9)
= 3(9) + 5
= 27 + 5
= 32
Therefore, (f o g)(-3) = 32.