Question

If f is an invertible function, defined as f(x) = $\frac{3x-4}{5}$, then write $f^{-1}(x).$

Let A = {1, 2, 3, 4}. Let R be the equivalence relation on A × A defined by (a, b)R(c, d) if a + d = b + c. Find the equivalence class [(1,3)].

If $\left(\begin{array}{l l }x-y & z \\ 2x-y & w\end{array}\right)$ = $\left(\begin{array}{l l }-1 & 4 \\ 0 & 5\end{array}\right)$ , find the value of x + y.

If f : R → R is defined by f(x) = 3x + 2, then define f [f(x)].

Write the degree of the differential equation : $\left(\frac{d y}{d x}\right)^{4}+3x\frac{d^{2}y}{d x^{2}}=0.$

If 2 $\left(\begin{array}{l l }1 & 3 \\ 0 & x\end{array}\right)$ + $\left(\begin{array}{l l }y & 0 \\ 1 & 2\end{array}\right)$ = $\left(\begin{array}{l l }5 & 6 \\ 1 & 8\end{array}\right)$ , write the value of (x + y).

If 3A – B = $\left(\begin{array}{l l }5 & 0 \\ 1 & 1\end{array}\right)$ and B = $\left(\begin{array}{l l }4 & 3 \\ 2 & 5\end{array}\right)$ , then find the matrix A.