Let g(x) be a rational function with a numerator of 6x2 + 12x - 48 and a denominator of 2x2 - 8. Use this information to evaluate g(8).
g(8)=(6*64+96+48)/(128-8)
= noting all numbers are even
= (3*64+48+24)/60
dividing again
=(3*32+24+12)/30
again= (3*16+12+6)/15=66/15=4 6/15
= 4 2/5
To evaluate g(8), we need to substitute x = 8 into the rational function g(x).
First, let's write out the rational function g(x):
g(x) = (6x^2 + 12x - 48) / (2x^2 - 8)
Now we substitute x = 8 into the function:
g(8) = (6(8)^2 + 12(8) - 48) / (2(8)^2 - 8)
Evaluating the numerator:
6(8)^2 + 12(8) - 48 = 6(64) + 12(8) - 48 = 384 + 96 - 48 = 432
Evaluating the denominator:
2(8)^2 - 8 = 2(64) - 8 = 128 - 8 = 120
Now we can substitute the values into the function:
g(8) = 432 / 120
To simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which in this case is 24:
g(8) = (432 / 24) / (120 / 24) = 18 / 5
Therefore, g(8) = 18 / 5.