Question

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

If the determinant of matrix A of order 3 × 3 is of value 4, write the value of |3A|.

If matrix A = $\left(\begin{array}{l l }3 & -3 \\ -3 & 3\end{array}\right)$ and A² = λA, then write the value of λ.

If $\begin{vmatrix} \sin\alpha & \cos\beta \\ \cos\alpha & \sin\beta \end{vmatrix} =-\ {\begin{array}{l}{1}\\ {2}\end{array}}\$ , write the value of x.

If A, B and C are the vertices of a $\Delta A B C$, then what is the value of ${\vec{AB}}+{\vec{BC}}+{\vec{C A}}$ ?

What is the degree of the following differential equation ? $5x\biggl(\frac{d y}{d x}\biggr)^{2}-\frac{d^{2}y}{d x^{2}}-6y\;=\log x.$

Give an example of a skew symmetric matrix of order 3.