Question

If f(x) = x2-9/x+5, find f(0), f(-1), f(1/k)

Answer 1

Explanation:

To find the values of f(x) at the given points, we substitute the values of x into the expression for f(x) and simplify:

f(x) = (x^2 - 9)/(x + 5)

a) To find f(0), we substitute 0 for x:

f(0) = (0^2 - 9)/(0 + 5) = -9/5

Therefore, f(0) = -1.8.

b) To find f(-1), we substitute -1 for x:

f(-1) = (-1^2 - 9)/(-1 + 5) = (-10)/4

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor of 2:

f(-1) = -5/2

Therefore, f(-1) = -2.5.

c) To find f(1/k), we substitute 1/k for x:

f(1/k) = ((1/k)^2 - 9)/(1/k + 5)

We can simplify the numerator by multiplying out the square:

f(1/k) = (1/k^2 - 9)/(1/k + 5)

We can simplify the denominator by multiplying by k/k:

f(1/k) = (1 - 9k^2)/(1 + 5k)

Therefore, f(1/k) = (1 - 9k^2)/(1 + 5k).

Answer 2

Explanation:

f(0):

f(0) = (0^2 - 9) / (0 + 5)

= -9/5

f(-1):

f(-1) = ((-1)^2 - 9) / (-1 + 5)

= (-8) / 4

= -2

f(1/k):

f(1/k) = ((1/k)^2 - 9) / (1/k + 5)

= (1/k^2 - 9) / (1/k) + 5

= (1 - 9k^2) / (k^2 + 5k)

Therefore, f(0) = -9/5, f(-1) = -2, and f(1/k) = (1 - 9k^2) / (k^2 + 5k).