Question

If $f(2x+3)=\sin x+2x,$ then,$f(4m-2n+3)$is equal to

Answer 1

Finding the value of $f(4m-2n+3)$:

Given that $f(2x+3)=\sin x+2x,$

$$\begin{gathered} f(4m–2n+3)=f\left(2\right(2m–n)+3) \\ =\sin (2m-n)+2^{(2m-n)} \\ f(4m–2n+3)=\sin (2m–n)+2^{(2m-n)} \end{gathered}$$

Hence, the value of $\mathbf{}\mathit{f}\mathbf{}\mathbf{(}\mathbf{4}\mathit{m}\mathbf{}\mathbf{-}\mathbf{2}\mathbf{}\mathit{n}\mathbf{+}\mathbf{3}\mathbf{)}\mathbf{}$ is $\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathbf{(}\mathbf{2}\mathit{m}\mathbf{}\mathbf{–}\mathbf{}\mathit{n}\mathbf{)}\mathbf{}\mathbf{+}\mathbf{}{\mathbf{2}}^{\mathbf{(}\mathbf{2}\mathbf{m}\mathbf{-}\mathbf{n}\mathbf{)}\mathbf{}\mathbf{}}$.