Homework help quick
given f(x)= (X+1)/(x) and g(x)= x squared +1 find (g f)(-9)
the options are
145/21
83/82
145/64
17/9
this is a homework question and it is due tommorow can u also explain or sow how you arrived at that answer
Thanks in advance
To find (g ∘ f)(-9), we first need to evaluate f(-9) and then substitute the result into g(x).
Given f(x) = (x + 1)/x, we substitute -9 for x:
f(-9) = (-9 + 1)/(-9)
= (-8)/(-9)
= 8/9
Now we have f(-9) = 8/9.
Next, we substitute this value into g(x):
g(f(-9)) = g(8/9)
Given g(x) = x^2 + 1, we substitute 8/9 for x:
g(8/9) = (8/9)^2 + 1
= 64/81 + 1
To simplify the fraction, we need a common denominator:
64/81 + 81/81
= (64 + 81)/81
= 145/81
Therefore, (g ∘ f)(-9) = 145/81.
Out of the options provided, none match the value 145/81. It is possible that there may be an error in the provided options or the question itself. I would recommend checking the options again or consulting with your teacher if you believe there may be a mistake.
Remember to always double-check the options and answers for accuracy.