Question

When f(x) is divided by (x - 2) the quotient is g(x) and the reamidner is 7. When g(x) is divided by (x - 4) the quotient is h (x) and the remainder is - 5 . What is the value of f(4) ?

Answer 1

To find f(4), we utilize the given relationships between the functions: f(x) = (x - 2)g(x) + 7 and g(x) = (x - 4)h(x) - 5. Substituting x with 4 and simplifying reveals that f(4) is -3.

Step-by-step explanation:

Given the division of a function f(x) by (x - 2) we have a quotient g(x) and a remainder 7. This can be expressed as:

f(x) = (x - 2)g(x) + 7

Furthermore, dividing g(x) by (x - 4) we get a quotient h(x) and a remainder -5, which can be represented as:

g(x) = (x - 4)h(x) - 5

To find f(4), we substitute x with 4:

f(4) = (4 - 2)g(4) + 7

Now, we look at g(x) at x = 4:

g(4) = (4 - 4)h(4) - 5

Since (4 - 4) = 0, this simplifies to g(4) = -5. Substituting back into f(4):

f(4) = (4 - 2)(-5) + 7 = -10 + 7 = -3. Hence, the value of f(4) is -3.