Property 12
Example
\(f(x)=\samefrac{2x-1}{3x+7}\Rightarrow f(x+3)=?\)
Solution
When \(f(x)\) is given and \(f(x+3)\) is asked, x+3 is substituted in place of x.
\(f(x+3)=\samefrac{2(x+3)-1}{3(x+3)+7}\Rightarrow f(x+3)=\samefrac{2x+5}{3x+16}\)
1.
\(f:\mathbb{R}\to \mathbb{R}\)
\(f(x)=2x+1\)
\(\Rightarrow f(x+1)=?\)
2.
\(f:\mathbb{R}\to \mathbb{R}\)
\(f(x)=3x+4\)
\(\Rightarrow f(x-2)=?\)
3.
\(f:\mathbb{R}\to \mathbb{R}\)
\(f(x)=3x+1\)
\(\Rightarrow f(x+1)=?\)
4.
\(f:\mathbb{R}\to \mathbb{R}\)
\(f(x)=2x+1\)
\(\Rightarrow f(x-1)=?\)
5.
\(f:\mathbb{R}\to \mathbb{R}\)
\(f(x)=x^2-3\)
\(\Rightarrow f(x+1)=?\)
6.
\(f:\mathbb{R}\to \mathbb{R}\)
\(f(x)=3x+6\)
\(\Rightarrow f(x^2)=?\)
7.
\(f:\mathbb{R}\to \mathbb{R}\)
\(f(x)=x-5\)
\(\Rightarrow f(x^2+2)=?\)
Property 13
To find \(f(x)\) when \(f(ax+b)\) is known, \(\samefrac{x-b}{a}\) which is the inverse of ax+b is substituted in place of x.
1.
\(f(x+1)=3x-7\)
\(\Rightarrow f(x)=?\)
2.
\(f(x-2)=2x-7\)
\(\Rightarrow f(x)=?\)
3.
\(f(2x-1)=4x+3\)
\(\Rightarrow f(x)=?\)
4.
\(f\left(\samefrac{2x-1}{3}\right)=\samefrac{4x+1}{2x-1}\)
\(f(x)=?\)
5.
\(f\left(\samefrac{x-1}{3}\right)=x^2+x\)
\(\Rightarrow f(x)=?\)