The above graph shows fx on the interval -6 - x - 6- If f3 - a- find the value of fa-

The correct option is D 2 #160;x #160; 6 5 4 30 #160;1 #160;23 4 5 6 #160;y #160;02 3 #160; 13 1 1 5 3 5 1 From the graph we form the t ...

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Byju's Answer

Standard XII

Mathematics

Definition of Functions

The above gra...

Question

The above graph shows $f (x)$ on the interval $- 6 \leq x \leq 6$ . If $f (3) = a$ , find the value of $f (a)$ .

-6

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-5

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Solution

The correct option is D 2
x -6 -5
-4
-3
0
1 2 3
4
5
6
y 0 2
-3
-1 3
-1
-1
-5
-3
5
-1
From the graph we form the table above.
As per the condition,
$f (3) = a$
when y = 3, a = -5
$f (- 5) = ?$
when x = -5
So, $f (- 5) = 2$

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y = f (s)

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According to LMVT, if a function f(x) is continuous on [a, b] and differentiable on the interval (a, b) then which of the following option should be correct for some value c from the interval (a,b)?( c can take any value from the interval (a,b) )

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f (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \begin{matrix} 1 + sin \frac{π}{2} x, f o r & - \infty < x \leq 1 \end{matrix} \begin{matrix} a x + b, f o r & 1 < x < 3 \end{matrix} \begin{matrix} 6 tan \frac{π x}{12}, f o r & 3 \leq x < 6 \end{matrix} \end{matrix}

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The above graph shows f(x) on the interval −6≤x≤6. If f(3)=a, find the value of f(a).

The correct option is D 2 x -6-5 -4-30 1 23 4 5 6 y 02 -3 -13 -1 -1 -5 -3 5 -1 From the graph we form the table above.As per the condition, f(3)=awhen y = 3, a = -5f(−5)=?when x = -5So, f(−5)=2

The above graph shows $f (x)$ on the interval $- 6 \leq x \leq 6$ . If $f (3) = a$ , find the value of $f (a)$ .

The correct option is D 2
x -6 -5
-4
-3
0
1 2 3
4
5
6
y 0 2
-3
-1 3
-1
-1
-5
-3
5
-1
From the graph we form the table above.
As per the condition,
$f (3) = a$
when y = 3, a = -5
$f (- 5) = ?$
when x = -5
So, $f (- 5) = 2$