If the function f is defined by
f(x+2) = 2x2 + 7x−5. Find F(-1).
To find F(-1), we substitute x = -1 into the equation for f(x+2):
F(-1+2) = 2(-1)^2 + 7(-1) - 5
F(1) = 2(1) + (-7) - 5
F(1) = 2 - 7 - 5
F(1) = -10
Therefore, F(-1) = -10.
To find the value of f(-1), we need to substitute x = -1 into the given function f(x+2) = 2x^2 + 7x - 5.
Step 1: Substitute x = -1 into the function:
f((-1)+2) = 2(-1)^2 + 7(-1) - 5
Step 2: Simplify the expression inside the function:
f(1) = 2(1) + (-7) - 5
Step 3: Perform the calculations:
f(1) = 2 - 7 - 5
Step 4: Continue simplifying:
f(1) = -12
Therefore, f(-1) = -12.