Question

let f be a function from R to R defined by f(x)=3x-5 find the values of a and b given that (a, 4) and (1,b) belong to f.​

Answer 1

SOLUTION

GIVEN

Let f be a function from R to R defined by f(x)=3x-5

TO DETERMINE

The values of a and b given that (a, 4) and (1,b) belong to f.

EVALUATION

Here the given function is

$\sf{f(x) = 3x - 5 \: \: \: ......(1)}$

Now (a, 4) ∈ f

∴ f(a) = 4

$\implies \sf{3a - 5 = 4}$

$\implies \sf{3a = 9}$

$\implies \sf{a = 3}$

∴ a = 3

Again (1, b) ∈ f

$\implies \sf{(3 \times 1)- 5 = b}$

$\implies \sf{3- 5 = b}$

$\implies \sf{ - 2= b}$

$\implies \sf{b = - 2}$

∴ b = - 2

FINAL ANSWER

a = 3 & b = - 2

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Answer 2

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f(x)=3x−5. ----- Eq(1)

Now (a, 4) ∈ f

∴ f(a) = 4

→ 3a− 5 =4

→ 3a =5+4

→ 3a = 9

→ a =9/3

→ a= 3

∴ a = 3

Again (1, b) ∈ f

→ (3×1)− 5= b

→ 3 −5 =b

→ −2= b

→ b= −2

∴ b = - 2

a = 3 & b = - 2