Question

If g(n)=-3/(n+2) and h(n)=-n, for what real value of x is g(x)=h(x)?

1) 1 only
2) 3 only
3) -1 and 3 only
4) 1 and -3 only

Answer 1

To determine the real value of x where g(x) = h(x), we equate -3/(x+2) to -x, simplify, and solve the resulting quadratic equation, yielding x = -3 and x = 1 as the solutions.

Step-by-step explanation:

The question asks for the real value of x where the two functions g(x) and h(x) are equal. Function g(x) is defined as g(x) = -3/(x+2) and function h(x) is defined as h(x) = -x. To find the real value of x, we need to set g(x) equal to h(x) and solve for x.

Equating the two functions gives us:

-3/(x+2) = -x

By multiplying both sides by (x+2) to eliminate the fraction, we get:

-3 = -x(x+2)

Expanding the right side gives us:

-3 = -x^2 - 2x

Putting every term to one side, we get:

x^2 + 2x - 3 = 0

Factoring the quadratic equation, we find:

(x + 3)(x - 1) = 0

This gives us two possible solutions for x:

• x = -3
• x = 1

Therefore, the real values of x where g(x) equals h(x) are -3 and 1.