Question

Determine whether each function is even, odd, or neither.

Answer 1

Answer:

a)  f(x) = x² -9

function is an even function

b)  g(x) = |x -3|

function is an even function

c) f(x)= x / x²-1

function is  odd function

d) g(x) = x + x²

Given function is not an even not odd function

This function is neither even or odd

Step-by-step explanation:

Explanation:-

a) Given f(x) = x² -9

Even function

If f(-x) = f(x) , then the function is even function.

f(-x) = (-x)² -9

      =  x² -9

      = f(x)

f(-x) = f(x)

∴ Given function is an even function

b)

Given g(x) = |x -3|

Even function

If g(-x) = g(x) , then the function is even function.

g(-x) = |-(x-3)|

      = |x-3|

g(-x) = g(x)

∴ Given function is an even function

c)

odd function

If f(-x) =- f(x) , then the function is odd function.

f(-x) = $f(-x) = \frac{-x}{(-x)^{2}+1 } = \frac{-x}{x^{2}+1 } = - f(x)$

      = -f(x)

f(-x) = -f(x)

∴ Given function is odd function

d)

If g(-x) = g(x) , then the function is even function.

g(x) = x + x²

g(-x) =  -x + (-x)²

     = - (x - x²)

This is not either even or odd function

∴ Given function is neither function