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1 vote

**Answer the question based on the following information.**

In each of the following questions, a pair of graphs F(x) and F1(x) is given. These are composed of straight-line segments, shown as solid lines, in the domain x $\in (2, -2).$

Choose the answer as

- if F1(x) = –F(x)
- if F1(x) = F(–x)
- if F1(x) = –F(–x)
- if none of the above is true

3 votes

Lets examine each option :

$\text{Option (A)}:$ F1(x) = –F(x) ; it will result the graph mirror image with respect to X -axis . So when we take the mirror image of F(x) with respect to X axis . we didnt get F1(x) . so option a is wrong

$\text{Option (B)}:$ F1(x) = F(–x) ; it will copy the graph which is left to y axis to right to y axis and vice versa . As f(x) is symmetric to y axis . so you will not see any change in the graph of F(–x) . so this option is also not correct .

$\text{Option (C)}:$ F1(x) = –F(–x) ; as we know from option b that F(-x) is same as F(x) . so -F(-x) will be same as option a . so this one is also not correct .

So, answer is option $\text{D (None) }$

$\text{Option (A)}:$ F1(x) = –F(x) ; it will result the graph mirror image with respect to X -axis . So when we take the mirror image of F(x) with respect to X axis . we didnt get F1(x) . so option a is wrong

$\text{Option (B)}:$ F1(x) = F(–x) ; it will copy the graph which is left to y axis to right to y axis and vice versa . As f(x) is symmetric to y axis . so you will not see any change in the graph of F(–x) . so this option is also not correct .

$\text{Option (C)}:$ F1(x) = –F(–x) ; as we know from option b that F(-x) is same as F(x) . so -F(-x) will be same as option a . so this one is also not correct .

So, answer is option $\text{D (None) }$