Find the values of a in the domain of f for which f(a)equals the given number.
f(x) = |x + 5|; f(a) = 9
If |a+5| = 9, either
a+5 = 9
or
a+5 = -9
So, a = 4 or -14
To find the values of 'a' in the domain of f for which f(a) equals 9, we need to solve the equation:
|a + 5| = 9
To remove the absolute value, we can rewrite the equation as two separate cases:
1. a + 5 = 9
2. -(a + 5) = 9
For the first case, solving for 'a' gives:
a + 5 = 9
a = 9 - 5
a = 4
For the second case, solving for 'a' gives:
-(a + 5) = 9
-a - 5 = 9
-a = 9 + 5
-a = 14
a = -14 (Remember to switch the sign when dividing by -1.)
Therefore, the values of 'a' in the domain of f for which f(a) equals 9 are a = 4 and a = -14.