Property 20
Linear Function
\(f:\mathbb{R}\to \mathbb{R}\)
\(\begin{aligned}y&=f(x)\\\samefrac{x}{a}+\samefrac{y}{b} &=1\end{aligned}\)
Functions defined as \(f(x)=ax+b\) are called linear functions. If any two points of a linear function are known as the general equation of the function can be determined.
Linear functions which are defined from \(\mathbb{R}\) to \(\mathbb{R}\) are given below.
1.
\(f(1)=3\)
\(f(2)=6\)
\(\Rightarrow f(3)=?\)
2.
\(f(1)=6\)
\(f(3)=10\)
\(\Rightarrow f(5)=?\)
3.
\(f(0)=-1\)
\(f(2)=5\)
\(\Rightarrow f(3)=?\)
4.
\(f(1)=-7\)
\(f^{-1}(-5)=3\)
\(\Rightarrow f(2)=?\)
5.
\(f(1)=5\)
\(f(3)=11\)
\(\Rightarrow f(x)=?\)
6.
\(f(3)=17\)
\(f(1)=7\)
\(\Rightarrow f(x)=?\)
7.
\(f(x+1)+f(x-1)=4x+2\)
\(\Rightarrow f(1)=?\)
8.
\(f(x-2)+f(x+2)=6x+4\)
\(\Rightarrow f(4)=?\)
9.
\(\Rightarrow f(x)=?\)
10.
\(\Rightarrow f(x)=?\)
11.
\(\Rightarrow f(2)=?\)
12.
\(\Rightarrow f(4)=?\)