I know where to even start these 3 problems
The given is this:Let f(x)=x^2+3 and g(x)=4x+2, evaluate the following.
c. 2*f(x)-g(x) =
d.f(g(4)) =
e.g(f(4)) =
huh? just do a direct substitution...
2*f(x)-g(x) = 2*(x^2+3)-(4x+2) = ...
f(g(4)) = f(4*4+2) = f(18) = ...
g(f(4)) = g(4^2+3) = g(19) = ...
don't be scared by all those parentheses...
f(x) = x² + 3
g(x) = 4 x + 2
c.
2 ∙ f(x) - g(x) = 2 ∙ ( x² + 3 ) - ( 4x + 2 ) = 2 x² + 6 - 4 x - 2 =
2 x² - 4 x + 4 = 2 ( x² - 2 x + 2 )
d.
g(4) = 4 ∙ 4 + 2 = 16 + 2 = 18
f(g(4)) = f (18) = 18² + 3 = 324 + 3 = 327
e.
f(4) = 4² + 3 = 16 + 3 + 19
g(f(4)) = g(19) = 4 ∙ 19 + 2 = 76 + 2 = 78
My typo.
f(4) = 4² + 3 = 16 + 3 = 19
To evaluate the expressions, we need to substitute the given functions into the expressions and simplify. Let's break down each problem and solve them step by step.
c. 2*f(x) - g(x)
Step 1: Start by substituting the given functions into the expression.
2*f(x) - g(x) = 2*(x^2 + 3) - (4x + 2)
Step 2: Simplify the expression.
2*(x^2 + 3) - (4x + 2) = 2x^2 + 6 - 4x - 2
Step 3: Combine like terms to obtain the final result.
2x^2 + 6 - 4x - 2 = 2x^2 - 4x + 4
Therefore, 2*f(x) - g(x) simplifies to 2x^2 - 4x + 4.
d. f(g(4))
Step 1: Start by substituting the value 4 into the function g(x).
g(4) = 4*(4) + 2
Step 2: Simplify the expression.
4*(4) + 2 = 16 + 2 = 18
Step 3: Substitute the result of g(4) into the function f(x).
f(g(4)) = f(18)
Step 4: Substitute the value 18 into the function f(x).
f(18) = (18)^2 + 3
Step 5: Simplify the expression.
(18)^2 + 3 = 324 + 3 = 327
Therefore, f(g(4)) = 327.
e. g(f(4))
Step 1: Start by substituting the value 4 into the function f(x).
f(4) = (4)^2 + 3
Step 2: Simplify the expression.
(4)^2 + 3 = 16 + 3 = 19
Step 3: Substitute the result of f(4) into the function g(x).
g(f(4)) = g(19)
Step 4: Substitute the value 19 into the function g(x).
g(19) = 4*(19) + 2
Step 5: Simplify the expression.
4*(19) + 2 = 76 + 2 = 78
Therefore, g(f(4)) = 78.
I hope this explanation helps you understand how to approach and solve these problems. If you have any further questions, please let me know.