1
MHT CET 2023 11th May Evening Shift
+2
-0

If $$\mathrm{f}(x)=\frac{3 x+4}{5 x-7}$$ and $$\mathrm{g}(x)=\frac{7 x+4}{5 x-3}$$, then $$\mathrm{f}(\mathrm{g}(x))=$$

A
$$\frac{x^3+1}{x^2+2}$$
B
$$41 x$$
C
$$\mathrm{g}(\mathrm{f}(x))$$
D
$$\frac{5 x-7}{41}$$
2
MHT CET 2023 11th May Morning Shift
+2
-0

The domain of the function given by $$2^x+2^y=2$$ is

A
$$0< x \leq 1$$
B
$$0 \leq x \leq 1$$
C
$$-\infty < x \leq 0$$
D
$$-\infty < x < 1$$
3
MHT CET 2023 10th May Evening Shift
+2
-0

Let $$\mathrm{f}(x)=\mathrm{e}^x-x$$ and $$\mathrm{g}(x)=x^2-x, \forall x \in \mathrm{R}$$, then the set of all $$x \in \mathrm{R}$$, where the function $$\mathrm{h}(x)=(\mathrm{fog})(x)$$ is increasing is

A
$$\left[0, \frac{1}{2}\right] \cup[1, \infty)$$
B
$$\left[-1,-\frac{1}{2}\right] \cup\left[\frac{1}{2}, \infty\right)$$
C
$$[0, \infty)$$
D
$$\left[-\frac{1}{2}, 0\right] \cup[1, \infty)$$
4
MHT CET 2023 10th May Morning Shift
+2
-0

$$\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R} ; \mathrm{g}: \mathrm{R} \rightarrow \mathrm{R}$$ are two functions such that $$\mathrm{f}(x)=2 x-3, \mathrm{~g}(x)=x^3+5$$, then $$(\mathrm{fog})^{-1}(-9)$$ is

A
$$-2$$
B
2
C
$$-\sqrt{2}$$
D
$$\sqrt{2}$$
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