If a function f - R - R be defined by f x - left begin matrix 3 x-2- x0lendmatrix right- Find - f 1- f -1- f 0- f 2

We have, f(x) = { 3x 2, x lt;0 1,x = 0 4x+1, x gt;0 . Now, f(1) = 4 × 1 + 1 = 5, f( 1) = 3 × ( 1) 2 = 3 2= 5, f(0) = 1, and, f(2) = 4x 2 + 1 = 9 ∴ f(1) ...

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Standard XII

Mathematics

Range

If a function...

Question

If a function $f : R \to R$ be defined by
f(x) =3x-2, x<0
1,x = 0
4x+1, x>0
Find : f(1), f(-1), f(0), f(2)

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Solution

We have,
f(x) = 3x-2, x<0
1,x = 0
4x+1, x>0
Now,
$f (1) = 4 \times 1 + 1 = 5$ ,
$f (- 1) = 3 \times (- 1) - 2 = - 3 - 2 = - 5$ ,
$f (0) = 1,$
and, f(2) = 4x 2 + 1 = 9
$∴$ f(1) = 5, f(-1) = -5,
f(0) = 1, f(2) = 9

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If a function f:R→R be defined by f(x) =3x-2, x<0 1,x = 0 4x+1, x>0Find : f(1), f(-1), f(0), f(2)

We have, f(x) = 3x-2, x<0 1,x = 0 4x+1, x>0 Now, f(1)=4×1+1=5, f(−1)=3×(−1)−2=−3−2=−5, f(0)=1, and, f(2) = 4x 2 + 1 = 9 ∴ f(1) = 5, f(-1) = -5, f(0) = 1, f(2) = 9

If a function $f : R \to R$ be defined by
f(x) =3x-2, x<0
1,x = 0
4x+1, x>0
Find : f(1), f(-1), f(0), f(2)

We have,
f(x) = 3x-2, x<0
1,x = 0
4x+1, x>0
Now,
$f (1) = 4 \times 1 + 1 = 5$ ,
$f (- 1) = 3 \times (- 1) - 2 = - 3 - 2 = - 5$ ,
$f (0) = 1,$
and, f(2) = 4x 2 + 1 = 9
$∴$ f(1) = 5, f(-1) = -5,
f(0) = 1, f(2) = 9