What values of x can be used as input for the function? g(-5) and g(a+1) are the function values when x=-5 and x=a+1. The equations g(x)=32 and g(x)=0 are quadratic equations.
Domain: All real numbers Range: g(x)≥ 0 Values:
g(-5)=8
g(a+1)=2a^2+16a+32
g(x)=32 for x=-7 and x=1
g(x)=0 for x=-3
Practice makes perfect
Here we have many questions in the same exercise. Let's answer them one at the time.
Domain
The domain is all x-values than can be used as input for the function. There is no x-value where the expression becomes undefined. Therefore, the domain is all real numbers.
All real numbers
Range
The range is all function values that can be obtained. Consider the expression (x+3)^2. A squared number is always greater than or equal to 0. Therefore, 2(x+3)^2 is always greater than or equal to 0, no matter what x is. Therefore, the range can be described as follows.
g(x)≥ 0
Output Values
The expression g(-5) and g(a+1) is the function value when x=-5 and x=a+1. Let's substitute this value and expression for x and evaluate.
x
2(x+3)^2
g(x)
-5
2( -5+3)^2
8
To calculate g(a+1), we need to perform a few more calculation steps.
