Final answer:
To calculate (f o g)(-3), first evaluate g(-3) which is -5. Next, plug this into f(x) to get f(-5), yielding a result of 121. Thus, the value of (f o g)(-3) is 121.
Step-by-step explanation:
The student is asking to calculate the composition of two functions, specifically (f o g)(-3), where f(x) = 5x² − 4 and g(x) = x − 2. The composition (f o g)(x) means we first apply g to x, and then apply f to the result of g(x).
Step 1: Evaluate g(-3), which gives -3 − 2 = -5.
Step 2: Substitute the g(-3) value into f, to get f(-5), which is 5(-5)² − 4.
Step 3: Calculate f(-5). Since (-5)² is 25, and 5×25 is 125, we have 5(-5)² − 4 equals 125 − 4, which is 121.
Therefore, the value of (f o g)(-3) is 121.