the function f and g are defined by
f(x)=1/2x+5 g(x)=x^2
Evaluate
1.g(3)
2. f inverse (6)
3.fg(2)
Iwill be happy to critique your work on this.
To evaluate the given expressions, we substitute the given values into the respective functions and simplify.
1. To evaluate g(3), we substitute 3 into the function g(x):
g(3) = (3)^2 = 9
Therefore, g(3) = 9.
2. To find the inverse of the function f, we need to solve for x in terms of f(x), which is 6 in this case:
f(x) = (1/2)x + 5
First, let's replace f(x) with 6:
6 = (1/2)x + 5
Next, we solve for x:
6 - 5 = (1/2)x
1 = (1/2)x
To isolate x, we divide both sides of the equation by (1/2):
(1/1) = (1/2)x / (1/2)
1 = x
Therefore, f^(-1)(6) = 1.
3. To evaluate fg(2), we need to compute the values of f(g(x)) and substitute 2 into the resulting equation:
First, calculate g(2) by substituting 2 into the function g(x):
g(2) = (2)^2 = 4
Next, evaluate f(g(2)) by substituting 4 into the function f(x):
f(g(2)) = (1/2)(4) + 5
= 2 + 5
= 7
Therefore, fg(2) = 7.