Answer:
Option c) is correct
ie., c=4 represents the value of c suchthat function
![f(c)=28](https://img.qammunity.org/2021/formulas/mathematics/high-school/tqefpnkuasnvqqrmkcysqis3szf1f4uvfb.png)
Explanation:
Given function f is defined by
![f(x)=2x^(2)-4](https://img.qammunity.org/2021/formulas/mathematics/high-school/wmc7bz4xotc4pafy0g4vzej3m49b8hiarj.png)
To find the value of "c" such that
![f(c)=28](https://img.qammunity.org/2021/formulas/mathematics/high-school/tqefpnkuasnvqqrmkcysqis3szf1f4uvfb.png)
Therefore put x=c in the given function as
![f(x)=2x^(2)-4](https://img.qammunity.org/2021/formulas/mathematics/high-school/wmc7bz4xotc4pafy0g4vzej3m49b8hiarj.png)
![f(c)=2c^(2)-4](https://img.qammunity.org/2021/formulas/mathematics/high-school/vo4w8f15p84z2pczm2hck10b66mgm8xyjb.png)
and we have
![f(c)=28](https://img.qammunity.org/2021/formulas/mathematics/high-school/tqefpnkuasnvqqrmkcysqis3szf1f4uvfb.png)
Now equating the two functions
![f(c)=2c^(2)-4=28](https://img.qammunity.org/2021/formulas/mathematics/high-school/iz10xowesbsuglvhft5ucpwdu94fpuulyn.png)
![2c^(2)-4=28](https://img.qammunity.org/2021/formulas/mathematics/high-school/hanrzn31jv4txkpu5st2kz1q365war5bz3.png)
![2c^(2)=28+4](https://img.qammunity.org/2021/formulas/mathematics/high-school/9nsfgx02tzyqgjhqum74oo5eu7uk4fgrcr.png)
![c^(2)=(32)/(2)](https://img.qammunity.org/2021/formulas/mathematics/high-school/capgvnqy8jo0kxenm9d5e93zcaan86rjs9.png)
![c^(2)=16](https://img.qammunity.org/2021/formulas/mathematics/high-school/mt82n6giri27lbsblwvupa66nxtoifbmwx.png)
![c=4](https://img.qammunity.org/2021/formulas/mathematics/high-school/vq3f73m7y1uunpskaldh70ii0ety879jdf.png)
Therefore
![c=4](https://img.qammunity.org/2021/formulas/mathematics/high-school/vq3f73m7y1uunpskaldh70ii0ety879jdf.png)
Option c) is correct
ie., c=4 represents the value of c suchthat function
![f(c)=28](https://img.qammunity.org/2021/formulas/mathematics/high-school/tqefpnkuasnvqqrmkcysqis3szf1f4uvfb.png)