To find the value of a function f(x) for a given value of x in the domain of f(x), we substitute the value of x in f(x) and evaluate the function. The function can evaluate to any value, either a positive or negative real number or zero if it is in the range of f(x).
Suppose a function p given by p=2d-1 represents the increase in price of a commodity with the number of years passed since 1999. If its cost was $35 in year 1999, find its current price.
Here d is the independent variable representing number of years since 1999 and p is the dependent variable representing price.
2010 - 1999=11 years, hence d=11
Using d as 11; increase in price = 2 x 11-1=21
Hence current price is 35 +21 =$56
Sometimes it will be required to find the value/values of x when f(x) is given. The number of values of x that we get depends on the maximum degree or power of expression for f(x).
Given that f(x) = x2 and f(x)=8. Find the value of x.
Whenever y=f(x) and f(x) is a polynomial function with highest degree n, then for a given value of y there will be n values of x possible.
When evaluating functions it is sometimes necessary to evaluate a function at a variable expression. Let us look at some examples.
Given f(x) = 3x + 4, find f(x + 2).
Here we substitute x + 2 in the original function wherever x was.
f (x + 2) = 3(x+2) + 4 = 3x + 6 + 4 = 3x + 10.
Given f(x) = 5x – 3, find f (2x).
Again, we substitute 2x wherever x was, so we get:
f(2x) = 5(2x) – 3 = 10x – 3.
Given f(x) = 17x3+ 5x, find f (-x).
f (-x) = 17(-x)3+ 5(-x) = -17x3 – 5x
Notice that in this case f (-x) = -f(x) since all the signs are flipped. –f(x) is called the opposite of f(x).
Try this question
- Evaluate f(x) = 2x – 1/4, find f(-x).
Answer: f (-x) = 2(-x) – ¼ = -2x -1/4