Fully Functioning

Algebra Level 2

When x = 15 x = 15 , f ( x ) = 25 f(x) = 25 . Given that function f f is a linear function and that f ( − 10 ) = 0 f(-10) = 0 , find f ( 1327 ) f(1327) .


The answer is 1337.

Goh Choon Aik by Goh Choon Aik , 21, Singapore

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2 solutions

Rishabh Jain
Jun 30, 2016

Let A ≡ ( 15 , 25 ) , B ≡ ( − 10 , 0 ) , C ≡ ( 1327 , α ) A\equiv(15,25),B\equiv(-10,0),C\equiv(1327,\alpha) .

Since function represents a straight line. ⟹ ( Slope ) A B = ( Slope ) B C \implies (\text{Slope})_{AB}=(\text{Slope})_{BC}

⟹ 25 − 0 15 − ( − 10 ) = α − 0 1327 − ( − 10 ) ( Point Slope Form ) \implies \dfrac{25-0}{15-(-10)}=\dfrac{\alpha-0}{1327-(-10)}\\~~~~~~(\small{\color{#20A900}{\text{Point Slope Form}}})

⟹ α = 1337 \implies \alpha=\boxed{1337}

6 Helpful 0 Interesting 0 Brilliant 0 Confused
Viki Zeta
Jun 30, 2016

f(x) is a linear function. So f(x) = ax + b; a,b are constant f ( 15 ) = 25 = 15 a + b . . . . ( 1 ) f ( − 10 ) = 0 = − 10 a + b . . . . ( 2 ) ( 1 ) − ( 2 ) = > 25 = 25 a = > a = 1 using a = 1 in (2) gives you b = 10 T h e r e f o r e , f ( x ) = x + 10 = > f ( 1327 ) = 1327 + 10 = 1337 \text{f(x) is a linear function. So f(x) = ax + b; a,b are constant} \\ f(15) = 25 = 15a + b .... (1)\\ f(-10) = 0 = -10a + b .... (2) \\ \text{ }\\ (1) - (2)\\ => 25 = 25a\\ => a = 1\\ \text{using a = 1 in (2) gives you} \\ b = 10\\ Therefore, f(x) = x + 10 \\ => f(1327) = 1327 + 10 = 1337

4 Helpful 0 Interesting 0 Brilliant 0 Confused

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