Question

If f : R → R defined as f(x) =${\frac{2x-7}{4}}\ $ is an invertible function, write $f^{-1}(x).$

Find the scalar components of the vector $\stackrel{\rightarrow}{A B}$ with initial point A(2,1) and terminal point B (– 5, 7).

Write a vector in the direction of the vector $\displaystyle{\hat{\iota}}-2\,{\hat{\iota}}+2\,{\hat{\iota}}$ that has magnitude 9 units.

If A is an invertible square matrix of order 3 and |A| = 5, then find the value of |adj A|.

Write the order of the differential equation: $\log\,\left(\frac{d^{2}y}{d x^{2}}\right)=\left(\frac{d y}{d x}\right)^{3}+x$

If A' = $\left(\begin{array}{l l }3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right)$ and B = $\left(\begin{array}{l l l }-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right)$ then find A' – B'.

Find the solution of the differential equation ${\frac{d y}{d x}}=x^{3}e^{-2y}$.