Evaluate the function at the given value of the independent variable and simplify.
f(x) = 2x2 - 5x + 6; f(x - 1)
f(x-1) = 2(x-1)^2 -5(x-1) + 6
= 2x^2 -4x +2 -5x + 1 +6
= 2x^2 -9x +9
Find and simplify f(x+h). Simplify your answer. f(x) =-4x^2+3x-5
To evaluate the function f(x) = 2x^2 - 5x + 6 at the given value of the independent variable (x - 1), we substitute (x - 1) wherever x occurs in the function and simplify the expression.
f(x - 1) = 2(x - 1)^2 - 5(x - 1) + 6
Now, let's simplify step by step:
First, we multiply out (x - 1)^2:
(x - 1)^2 = (x - 1)(x - 1) = x^2 - x - x + 1 = x^2 - 2x + 1
Substituting this back into the function:
f(x - 1) = 2(x - 1)^2 - 5(x - 1) + 6
= 2(x^2 - 2x + 1) - 5(x - 1) + 6
= 2x^2 - 4x + 2 - 5x + 5 + 6
= 2x^2 - 9x + 13
Therefore, f(x - 1) simplifies to 2x^2 - 9x + 13.
To evaluate the function f(x) = 2x^2 - 5x + 6 at the given value x - 1, we need to substitute x - 1 in place of x in the function and simplify the expression.
Let's substitute x - 1 in place of x:
f(x - 1) = 2(x - 1)^2 - 5(x - 1) + 6
Now, we simplify the expression using the following steps:
Step 1: Expand the squared term (x - 1)^2 using the formula (a - b)^2 = a^2 - 2ab + b^2.
(x - 1)^2 = x^2 - 2(x)(1) + 1^2 = x^2 - 2x + 1
Step 2: Substitute the expanded value of (x - 1)^2 in the expression:
f(x - 1) = 2(x^2 - 2x + 1) - 5(x - 1) + 6
Step 3: Distribute the coefficients:
f(x - 1) = 2x^2 - 4x + 2 - 5x + 5 + 6
Step 4: Combine like terms:
f(x - 1) = 2x^2 - 9x + 13
Therefore, the simplified expression for f(x - 1) is 2x^2 - 9x + 13.