Question

f(x)=2x-8 g(x)=x^(2) Find a value of x such that fg(x)=0. Give your answer as an integer or as a decimal.

Answer 1

To find the values of x that make fg(x) equal to 0, we substitute g(x) into the expression f(g(x)). We solve the resulting quadratic equation and find that x = 2 and x = -2.

Step-by-step explanation:

To find a value of x that makes the expression fg(x) equal to 0, we need to substitute the function g(x) into the expression f(g(x)).

Given f(x) = 2x - 8 and g(x) = x^2, we have:

f(g(x)) = 2(g(x)) - 8 = 2(x^2) - 8 = 2x^2 - 8

To find the value of x that makes 2x^2 - 8 equal to 0, we can set the expression equal to 0 and solve for x.

2x^2 - 8 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, factoring is not possible, so we'll use the quadratic formula:

• x = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 2, b = 0, and c = -8. Substituting these values into the quadratic formula:

• x = (-0 ± √(0^2 - 4(2)(-8))) / (2(2))

Simplifying:

• x = ± √(0 + 64) / 4

Which further simplifies to:

• x = ± √64 / 4

Finally, we can calculate the square root of 64 and divide by 4 to find the values of x:

• x = ±8 / 4

Therefore, the values of x that make fg(x) equal to 0 are x = 2 and x = -2.

Answer 2

`2 {x}^(2) (x - 4) = 0`

Step-by-step explanation:

`(2x - 8)(x ^(2) ) = 0`

`2x(x ^(2) ) - 8( {x}^(2) ) = 0`

`2 {x}^(2) = (0)/(x - 4)`