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.
Answers
Given,
A function f(x) = 3x-5.
To Find,
The value of a and b such that (a,4)and(1,b)belong to f.
Solution,
The function f(x) is 3x-5
Now, for point (a,4)
f(a) = 4
3a-5 = 4
3a = 9
a = 3
For point (1,b)
f(1) = b
3(1)-5 = b
-2 = b
Hence, the value of a is 3 and b is -2.
Answer:
According to given question, we have to find the values of a and b which will satisfy the function f(x) = 3x-5, if (a,4) as well as (1,b) belong to f.
Step-by-step explanation:
Given : The function as f(x) = 3x-5
The function being from R to R, i.e., from set of real numbers to set of real numbers. This means, the domain as well as the range of the function will contain real numbers, which can be rational as well as irrational.
To Find : Values of a as well as b if (a,4) and (1,b) belong to f, that means, satisfies the function.
Now, a and b satisfy the function.
We know that in cartesian system, we always right the domain first and then the range. This means in (a,4), a is the domain, whereas 4 is the range. Similarly, in (1,b), 1 is the domain and b is the range. Now, they satisfy the function means that the domains have unique images in the co-domain, named as range.
Therefore, for the first case, i.e, (a,4) we can write it as:
f(a) = (3×a) - 5
4 = 3a - 5
3a = 9
a = 3
Therefore, a = 3 is the correct answer and (3,4) belong to f.
Similarly, (1,b) belong to f:
f(1) = (3×1) - 5
b = 3 - 5
b = -2
Hence, b = -2 is the correct answer and (1,-2) belong to f as well.