Question

Seja uma função f:R→R tal que f(x)=ax+b, para a, b∈R. Sabendo que f(13)=188, f(10)=146, f(3)=n e f(m)=62. Qual o valor de m+n?

Answer 1

$\large\boxed{\begin{array}{l}\rm f(13)=188\longrightarrow A(13,188)\\\rm f(10)=146\longrightarrow B(10,146)\\\rm a=\dfrac{y_B-y_A}{x_B-x_A}\\\\\rm a=\dfrac{146-188}{10-13}=\dfrac{-42}{-3}=14\\\\\rm f(x)=ax+b\\\rm f(10)=14\cdot 10+b\\\rm 140+b=146\\\rm b=146-140\\\rm b=6\end{array}}$

$\large\boxed{\begin{array}{l}\rm f(x)=14x+6\\\rm f(3)=14\cdot3+6\\\rm n=42+6=48\\\rm f(m)=62\\\rm f(m)=14\cdot m+6\\\rm 14m+6=62\\\rm 14m=62-6\\\rm 14m=56\\\rm m =\dfrac{56}{14}\\\\\rm m=4\\\\\rm m+n=4+48\\\huge\boxed{\boxed{\boxed{\boxed{\rm m+n=52}}}}\end{array}}$