Find the values of a in the domain of f for which f(a)equals the given number. (If there is no solution, enter NO SOLUTION.)
f(x) = x2 − 4x − 19; f(a) = 13
a = ____ (smaller value)
a = ____ (larger value)
Use the following notation to show exponents
x^2 - 4x - 19 = 13
x^2 - 4x - 32 = 0
(x-8)(x+4) = 0
take over.
To find the values of a in the domain of f for which f(a) equals 13, we need to solve the equation f(a) = 13 using the given function f(x) = x^2 - 4x - 19.
So, we plug in 13 for f(a) in the equation and solve for a.
13 = a^2 - 4a - 19
Rearranging the equation, we get:
a^2 - 4a - 32 = 0
Now, we can solve this quadratic equation using factoring or the quadratic formula.
Factoring:
(a - 8)(a + 4) = 0
Setting each factor equal to zero gives us the solutions:
a - 8 = 0 -> a = 8
a + 4 = 0 -> a = -4
Therefore, the smaller value of a is -4 and the larger value of a is 8.
So, the values of a in the domain of f for which f(a) equals 13 are:
a = -4 (smaller value)
a = 8 (larger value)