Question

Given the function f(x) = 2x^2 + x - 1. Calculate the following values: a. f(0) = b. f(2) = c. f(-2) = d. f(x + 1) = e. f(-x)=

Answer 1

To calculate the given values for the function f(x) = 2x^2 + x - 1, substitute the given values of x into the function and solve for f(x).

Step-by-step explanation:

To calculate the given values for the function f(x) = 2x^2 + x - 1:

1. To find f(0), substitute x = 0 into the function and solve: f(0) = 2(0)^2 + 0 - 1 = -1.
2. To find f(2), substitute x = 2 into the function and solve: f(2) = 2(2)^2 + 2 - 1 = 9.
3. To find f(-2), substitute x = -2 into the function and solve: f(-2) = 2(-2)^2 - 2 - 1 = 7.
4. To find f(x + 1), substitute (x + 1) for x in the function and simplify: f(x + 1) = 2(x + 1)^2 + (x + 1) - 1 = 2x^2 + 6x + 2.
5. To find f(-x), substitute -x for x in the function and simplify: f(-x) = 2(-x)^2 - x - 1 = 2x^2 - x - 1.

Answer 2

The values are:
`a. \:1 ,\:\:b. \:9,\:\:c. \:5,\:\:d. \:2 x^2+5 x+2,\:\:e. \:2 x^2-x-1\:\:`

Given function:

`f(x) = 2x^2 + x - 1`

To find the the required values, Let's calculate each given case:

a. f(0):

This is evaluating the function
`f(x) = 2x^2 + x - 1` when x=0.

Substitute x=0 into the function:
`f(0)=2 \cdot 0^2+0-1=-1`

The result is -1.

b. f(2):

This is evaluating the function when x=2.

Substitute x=2 into the function:
`f(2)=2 \cdot 2^2+2-1=9`

The result is 9.

c. f(-2):

This is evaluating the function when x=-2.

Substitute x=-2 into the function:
`f(-2)=2 \cdot(-2)^2-2-1=5`

The result is 5.

d. f(x+1):

This is evaluating the function when x=x+1.

Substitute x=x+1 into the function:
`f(x+1)=2(x+1)^2+(x+1)-1`

Simplify to get
`f(-x)=2 x^2-x-1 .`

e. f(-x):

This is evaluating the function when x= -x.

Substitute x= -x into the function:
`f(-x)=2(-x)^2-x-1`

The result after simplifying is
`f(-x)=2 x^2-x-1 .`

Correct Question:

Given the function
`f(x) = 2x^2 + x - 1.`

Calculate the following values:

a. f(0)

b. f(2)

c. f(-2)

d. f(x + 1)

e. f(-x)=