Question

Prove that the function f : [0, ∞) → R given by f(x) = 9x² + 6x – 5 is not invertible. Modify the Codomain of the function f to make it invertible, and hence find f⁻¹.

A speaks truth in 60% of the cases, while B in 90% of cases. In what percent of cases are they likely to contradict each other in stating the same fact ? In the cases of contradiction do you think, the statement of B will carry more weight as he speaks truth in more number of cases than A ?

Evaluate : $\large\textstyle\int\!{\frac{\ d x}{x(x^{5}+3)}}\,.$

The total cost associated with provision of free mid-day meals to x students of a school in primary classes is given by C(x) = 0·005x³ – 0·02x² + 30x + 50. If the marginal cost is given by rate of change ${\frac{d c}{d x}}$ of total cost, write the marginal cost of food for 300 students.

Let R be a relation defined on the set of natural numbers N as follow : R = {(x, y) : $x\in N,y\in N$ and 2x + y = 24} Find the domain and range of the relation R. Also,find if R is an equivalence relation or not.

Evaluate : $\large\textstyle\int(x-3){\sqrt{x^{2}+3x-18}}\,d x\,.$

Find : $\textstyle\int$${\frac{x^{2}}{x^{4}+x^{2}-2}}d x$