Question

If f : R→ R defined by f(x) = $\textstyle{\frac{3x+5}{2}}$ is an invertible function, then find $f^{-1}(x).$

For what value of x, the matrix $\left(\begin{array}{l l }1+x & 7 \\ 3-x & 8\end{array}\right)$ is a singular matrix ?

If $|\stackrel{\rightarrow}{a}|$=2, $|\stackrel{\rightarrow}{b}|$=3 and $\stackrel{\rightarrow}{a}$.$\stackrel{\rightarrow}{b}$=3 then find the projection of $|\stackrel{\rightarrow}{b}|$ on $|\stackrel{\rightarrow}{a}|$.

Write the value of $\textstyle\int\!{\frac{\ d x}{x^{2}+16}}$

If m and n are the order and degree, respectively of the differential equation $\textstyle y\left({\frac{d y}{d x}}\right)^{3}+x^{3}\left({\frac{d^{2}y}{d x^{2}}}\right)^{2}-x y$= sin x, then write the value of m + n.

Let f : R → R be defined by f(x) = 3x² – 5 and g : R → R be defined by g(x) =${\frac{x}{x^{2}+1}}.$ find gof(x) .

Let R be the equivalence relation in the set A = {0, 1, 2, 3, 4, 5} given by R = {(a, b) : 2 divides (a –b)}. Write the equivalence class [0].