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Functions f(x)

Functions f(x)

A function can be written as f(x), which is shorthand for the function of x is such that followed by an expression for the function eg f(x)=2x+4. The right hand side states what will be done to x: multiply by 2 and add 4.

A function is written with a single letter (normally f) followed by a variable (normally x) in brackets on the left hand side of the equation sign; and an expression (the function to be applied to that variable) on the right hand side.

When a function is evaluated, replace the variable with the number: using the above function,

f(3)=2×3+4=10 or

f(-5)=2×-5+4=-6

Sometimes the function may be written slightly differently with a colon and an arrow:

x:2x+4 or even as x2x+4.

Example 1

f(x) is defined as f(x)=3x2+2.

What is the value of f(7)?

f(x)=3x2+2

f(7)=3(7)2+2

= 3 x 49 + 2

=149

Answer: 149

Example 2

Given a function f(x)=x2+4, find the value of f(7).

f(x)=x2+4

f(7)=72+4 (Replace x with 7)

=49+4

=53

Answer: 53