Question

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

If $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$ are perpendicular vectors, $|\stackrel{\rightarrow}{a}\$ + $\stackrel{\rightarrow}{b}|\$ = 13 and $|\stackrel{\rightarrow}{a}|\$ =5,find the value of $|\stackrel{\rightarrow}{b}|\$.

Evaluate: $\textstyle\int\cot{x}(cosec x-1)e^{x}d x$ .

If $\begin{array}{l l}{{\vec{a}=x\,\hat{i}+2\,\hat{j}-z\,\hat{k}~}}&{{\mathrm{and}~~~~\vec{b}=3\,\hat{i}-y\,\hat{j}+\hat{k}}}\end{array}$ are two equal vectors, then write the value of x + y + z.

Write the differential equation obtained by eliminating the arbitrary constant C in the equation representing the family of curves xy = C cos x.

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).

Write fog, if f : R → R and g : R → R are given by f(x) = |x| and g(x) = |5x - 2|.